Question

lcm of 4 and 10

Answer 1

To find the least common multiple (LCM) of 4 and 10, you can use the prime factorization method or the formula involving the greatest common divisor (GCD).

1. **Prime Factorization**:
- The prime factorization of 4 is \(2^2\).
- The prime factorization of 10 is \(2^1 \times 5^1\).

To find the LCM, take the highest power of each prime number:
- For \(2\), the highest power is \(2^2\).
- For \(5\), the highest power is \(5^1\).

Therefore, the LCM is:
\[
LCM = 2^2 \times 5^1 = 4 \times 5 = 20.
\]

2. **Using GCD**:
- First, find the GCD of 4 and 10. The GCD is 2.
- Use the formula:
\[
LCM(a, b) = \frac{a \times b}{GCD(a, b)}.
\]
So,
\[
LCM(4, 10) = \frac{4 \times 10}{2} = \frac{40}{2} = 20.
\]

Therefore, the LCM of 4 and 10 is **20**.